Faraday rotation, or the Faraday effect, is a magneto-optical phenomenon that, as a result of interaction between light and a magnetic field in a medium, causes a rotation of a polarization vector of light wave by a degree that is linearly proportional to the strength of a component of the magnetic field collinear with the direction of propagation of light. For example, the Faraday effect causes left and right circularly polarized light waves to propagate at slightly different speeds, a property known as circular birefringence. A given linear polarization vector can be presented as a composition of two circularly polarized components, the effect of a relative phase shift, induced by the Faraday effect onto the linearly polarized light wave, is to rotate the orientation of the light wave's vector of linear polarization.
The empirical angle of rotation of a linear polarization vector of a light wave is given by β=VBd, where β is the angle of rotation (in radians), V is the Verdet constant for the material through which the light wave propagates, B is the magnetic flux density in the direction of propagation (in teslas), and d is the length of the path (in meters). The Verdet constant reflects the strength of the Faraday effect for a particular material. The Verdet constant can be positive or negative, with a positive Verdet constant corresponding to a counterclockwise rotation when the direction of propagation is parallel to the magnetic field. The Verdet constant for most materials is extremely small and is wavelength-dependent. Typically, the longer the wavelength of light, the smaller the Verdet constant. It is appreciated that a desired angle of rotation can be achieved at a shorter distance during propagation through a material in which the Verdet constant is high.
The Faraday effect allows for the construction of a Faraday rotator, which is a principal component of a Faraday isolator, a device that transmits light in only one direction. Faraday rotators and Faraday isolators of the related are bulk, stand-alone devices that are not well suited for optical integration (such as, for example, integration with waveguide-based or fiber-optic based components) and, when incorporated into an integrated optical system, require free-space optical coupling with other components of the integrated system, thereby limiting a degree of the system miniaturization and causing coupling losses.